MinT - Best Known (237−111, 237, s)-Nets in Base 4

Best Known (237−111, 237, s)-Nets in Base 4

(237−111, 237, 130)-Net over F₄ — Constructive and digital

Digital (126, 237, 130)-net over F₄, using

t-expansion [i] based on digital (105, 237, 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]

(237−111, 237, 205)-Net over F₄ — Digital

Digital (126, 237, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−111, 237, 2680)-Net in Base 4 — Upper bound on s

There is no (126, 237, 2681)-net in base 4, because

1 times m-reduction [i] would yield (126, 236, 2681)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12368 784420 129070 314973 532094 911517 669056 426217 420105 566961 425466 870782 011867 448461 844926 740259 713332 723748 548012 767968 051675 574791 769308 017416 > 4²³⁶ [i]