MinT - Best Known (126, 239, s)-Nets in Base 4

Best Known (126, 239, s)-Nets in Base 4

(126, 239, 130)-Net over F₄ — Constructive and digital

Digital (126, 239, 130)-net over F₄, using

t-expansion [i] based on digital (105, 239, 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]

(126, 239, 201)-Net over F₄ — Digital

Digital (126, 239, 201)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 239, 2573)-Net in Base 4 — Upper bound on s

There is no (126, 239, 2574)-net in base 4, because

1 times m-reduction [i] would yield (126, 238, 2574)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195200 209194 579513 201203 546692 687577 371982 722886 684059 121068 460544 179567 765503 019564 298674 605315 076645 902595 888926 193186 238472 756069 483832 709664 > 4²³⁸ [i]