MinT - Best Known (30−26, 30, s)-Nets in Base 64

Best Known (30−26, 30, s)-Nets in Base 64

(30−26, 30, 104)-Net over F₆₄ — Constructive and digital

Digital (4, 30, 104)-net over F₆₄, using

t-expansion [i] based on digital (3, 30, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(30−26, 30, 129)-Net over F₆₄ — Digital

Digital (4, 30, 129)-net over F₆₄, using

net from sequence [i] based on digital (4, 128)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 4 and N(F) ≥ 129, using
  - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(30−26, 30, 1318)-Net in Base 64 — Upper bound on s

There is no (4, 30, 1319)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 1 537467 322310 155617 984816 524279 287040 370359 239850 129320 > 64³⁰ [i]