MinT - Best Known (175−107, 175, s)-Nets in Base 4

Best Known (175−107, 175, s)-Nets in Base 4

(175−107, 175, 66)-Net over F₄ — Constructive and digital

Digital (68, 175, 66)-net over F₄, using

t-expansion [i] based on digital (49, 175, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(175−107, 175, 99)-Net over F₄ — Digital

Digital (68, 175, 99)-net over F₄, using

t-expansion [i] based on digital (61, 175, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(175−107, 175, 607)-Net in Base 4 — Upper bound on s

There is no (68, 175, 608)-net in base 4, because

1 times m-reduction [i] would yield (68, 174, 608)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 577 538381 477742 983451 532784 914644 392673 978436 890907 287459 920315 413996 499802 040927 372126 982486 131901 511310 > 4¹⁷⁴ [i]