MinT - Best Known (28−20, 28, s)-Nets in Base 64

Best Known (28−20, 28, s)-Nets in Base 64

(28−20, 28, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 28, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 28, 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]

(28−20, 28, 258)-Net in Base 64 — Constructive

(8, 28, 258)-net in base 64, using

base change [i] based on digital (1, 21, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(28−20, 28, 289)-Net in Base 64

(8, 28, 289)-net in base 64, using

base change [i] based on digital (1, 21, 289)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(28−20, 28, 8197)-Net in Base 64 — Upper bound on s

There is no (8, 28, 8198)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 374 273070 898052 327941 254869 202352 815192 340489 148416 > 64²⁸ [i]