MinT - Best Known (16, 16+36, s)-Nets in Base 64

Best Known (16, 16+36, s)-Nets in Base 64

(16, 16+36, 177)-Net over F₆₄ — Constructive and digital

Digital (16, 52, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 52, 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+36, 260)-Net in Base 64 — Constructive

(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+36, 267)-Net over F₆₄ — Digital

Digital (16, 52, 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+36, 321)-Net in Base 64

(16, 52, 321)-net in base 64, using

4 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+36, 19790)-Net in Base 64 — Upper bound on s

There is no (16, 52, 19791)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 8349 825007 236661 393755 623687 992577 060451 134088 326608 555597 990361 866769 563929 186180 212975 637628 > 64⁵² [i]