MinT - Best Known (127, 127+97, s)-Nets in Base 4

Best Known (127, 127+97, s)-Nets in Base 4

(127, 127+97, 130)-Net over F₄ — Constructive and digital

Digital (127, 224, 130)-net over F₄, using

t-expansion [i] based on digital (105, 224, 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+97, 250)-Net over F₄ — Digital

Digital (127, 224, 250)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+97, 3875)-Net in Base 4 — Upper bound on s

There is no (127, 224, 3876)-net in base 4, because

1 times m-reduction [i] would yield (127, 223, 3876)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 182 343633 380496 351694 316056 648180 235778 005265 468453 137203 555748 826032 637585 295273 865730 572673 970768 184420 049572 237785 930291 749903 552496 > 4²²³ [i]