MinT - Best Known (256−141, 256, s)-Nets in Base 4

Best Known (256−141, 256, s)-Nets in Base 4

(256−141, 256, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(256−141, 256, 168)-Net over F₄ — Digital

Digital (115, 256, 168)-net over F₄, using

net from sequence [i] based on digital (115, 167)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(256−141, 256, 1341)-Net in Base 4 — Upper bound on s

There is no (115, 256, 1342)-net in base 4, because

1 times m-reduction [i] would yield (115, 255, 1342)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3357 539091 279112 883878 476642 254642 050430 394974 924103 781113 221796 506756 183657 092928 136800 214317 893403 182978 373003 147389 736261 935056 688433 050796 615026 415440 > 4²⁵⁵ [i]