MinT - Best Known (133, 258, s)-Nets in Base 4

Best Known (133, 258, s)-Nets in Base 4

(133, 258, 130)-Net over F₄ — Constructive and digital

Digital (133, 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]

(133, 258, 199)-Net over F₄ — Digital

Digital (133, 258, 199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 258, 2446)-Net in Base 4 — Upper bound on s

There is no (133, 258, 2447)-net in base 4, because

1 times m-reduction [i] would yield (133, 257, 2447)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53935 939038 511513 123053 126653 366342 384727 936970 239348 972010 181375 317541 490464 521187 360037 880354 998083 815161 478557 134720 764429 658130 181116 417754 476011 874280 > 4²⁵⁷ [i]