MinT - Best Known (233−127, 233, s)-Nets in Base 4

Best Known (233−127, 233, s)-Nets in Base 4

(233−127, 233, 130)-Net over F₄ — Constructive and digital

Digital (106, 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]

(233−127, 233, 144)-Net over F₄ — Digital

Digital (106, 233, 144)-net over F₄, using

t-expansion [i] based on digital (91, 233, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(233−127, 233, 1284)-Net in Base 4 — Upper bound on s

There is no (106, 233, 1285)-net in base 4, because

1 times m-reduction [i] would yield (106, 232, 1285)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 223918 559282 659454 798421 925512 058765 090193 498323 666074 148197 766045 552251 404198 521665 255042 062611 865959 668207 082869 327244 971501 020065 447680 > 4²³² [i]