MinT - Best Known (16, 16+34, s)-Nets in Base 64

Best Known (16, 16+34, s)-Nets in Base 64

(16, 16+34, 177)-Net over F₆₄ — Constructive and digital

Digital (16, 50, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 50, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(16, 16+34, 260)-Net in Base 64 — Constructive

(16, 50, 260)-net in base 64, using

2 times m-reduction [i] based on (16, 52, 260)-net in base 64, using
- base change [i] based on digital (3, 39, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(16, 16+34, 267)-Net over F₆₄ — Digital

Digital (16, 50, 267)-net over F₆₄, using

net from sequence [i] based on digital (16, 266)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 16 and N(F) ≥ 267, using
  - a curve from the manYPoints database [i]

(16, 16+34, 321)-Net in Base 64

(16, 50, 321)-net in base 64, using

6 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
- base change [i] based on digital (2, 42, 321)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(16, 16+34, 23374)-Net in Base 64 — Upper bound on s

There is no (16, 50, 23375)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 037556 864706 078572 453998 400012 494316 038514 477824 213282 407015 222096 647507 833221 619839 665576 > 64⁵⁰ [i]