MinT - Best Known (258−128, 258, s)-Nets in Base 4

Best Known (258−128, 258, s)-Nets in Base 4

(258−128, 258, 130)-Net over F₄ — Constructive and digital

Digital (130, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(258−128, 258, 185)-Net over F₄ — Digital

Digital (130, 258, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−128, 258, 2146)-Net in Base 4 — Upper bound on s

There is no (130, 258, 2147)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 218393 520279 172057 648676 744838 469039 068940 774480 392606 731416 198515 633501 133391 907558 539561 144324 516166 095270 576988 074871 106879 411132 694354 559578 192684 588719 > 4²⁵⁸ [i]