MinT - Best Known (132, 253, s)-Nets in Base 4

Best Known (132, 253, s)-Nets in Base 4

(132, 253, 130)-Net over F₄ — Constructive and digital

Digital (132, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(132, 253, 204)-Net over F₄ — Digital

Digital (132, 253, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 253, 2562)-Net in Base 4 — Upper bound on s

There is no (132, 253, 2563)-net in base 4, because

1 times m-reduction [i] would yield (132, 252, 2563)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53 325890 422718 644847 181108 044356 149970 178751 191607 470257 595275 576680 716895 915621 052195 520033 893298 086343 301961 931694 571590 622198 298991 698421 676191 217024 > 4²⁵² [i]