MinT - Best Known (121, 236, s)-Nets in Base 4

Best Known (121, 236, s)-Nets in Base 4

(121, 236, 130)-Net over F₄ — Constructive and digital

Digital (121, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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]

(121, 236, 180)-Net over F₄ — Digital

Digital (121, 236, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 236, 2187)-Net in Base 4 — Upper bound on s

There is no (121, 236, 2188)-net in base 4, because

1 times m-reduction [i] would yield (121, 235, 2188)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3110 621427 691495 868465 880834 566156 394961 916788 068755 655508 574974 047257 358402 408302 113337 455515 363036 966436 676022 502938 491284 065118 084688 810200 > 4²³⁵ [i]