MinT - Best Known (256−124, 256, s)-Nets in Base 4

Best Known (256−124, 256, s)-Nets in Base 4

(256−124, 256, 130)-Net over F₄ — Constructive and digital

Digital (132, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(256−124, 256, 198)-Net over F₄ — Digital

Digital (132, 256, 198)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−124, 256, 2391)-Net in Base 4 — Upper bound on s

There is no (132, 256, 2392)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13559 676775 667332 536883 683996 651115 237763 492198 287048 639053 707855 754258 224381 316476 976828 461501 749950 331747 942025 989898 070688 412791 628748 085421 831253 041320 > 4²⁵⁶ [i]