MinT - Best Known (233−111, 233, s)-Nets in Base 4

Best Known (233−111, 233, s)-Nets in Base 4

(233−111, 233, 130)-Net over F₄ — Constructive and digital

Digital (122, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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]

(233−111, 233, 192)-Net over F₄ — Digital

Digital (122, 233, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−111, 233, 2418)-Net in Base 4 — Upper bound on s

There is no (122, 233, 2419)-net in base 4, because

1 times m-reduction [i] would yield (122, 232, 2419)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 686616 889295 011171 231410 967122 249768 686665 254789 530148 230650 235328 795378 438698 605885 783258 438946 447550 396306 773221 597329 021499 127790 296960 > 4²³² [i]