MinT - Best Known (127, 127+107, s)-Nets in Base 4

Best Known (127, 127+107, s)-Nets in Base 4

(127, 127+107, 130)-Net over F₄ — Constructive and digital

Digital (127, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(127, 127+107, 219)-Net over F₄ — Digital

Digital (127, 234, 219)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+107, 3000)-Net in Base 4 — Upper bound on s

There is no (127, 234, 3001)-net in base 4, because

1 times m-reduction [i] would yield (127, 233, 3001)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 191 563007 243279 593290 262298 896100 624734 106538 102337 607291 286510 041040 228721 177512 388151 755749 803678 047572 292341 824517 655630 077155 876541 430624 > 4²³³ [i]