MinT - Best Known (75, 75+69, s)-Nets in Base 4

Best Known (75, 75+69, s)-Nets in Base 4

(75, 75+69, 104)-Net over F₄ — Constructive and digital

Digital (75, 144, 104)-net over F₄, using

t-expansion [i] based on digital (73, 144, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(75, 75+69, 124)-Net over F₄ — Digital

Digital (75, 144, 124)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+69, 1508)-Net in Base 4 — Upper bound on s

There is no (75, 144, 1509)-net in base 4, because

1 times m-reduction [i] would yield (75, 143, 1509)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 124 573598 233562 494977 034618 182581 664095 133393 734566 801648 054157 556676 949385 401431 252162 > 4¹⁴³ [i]