MinT - Best Known (179−124, 179, s)-Nets in Base 4

Best Known (179−124, 179, s)-Nets in Base 4

(179−124, 179, 66)-Net over F₄ — Constructive and digital

Digital (55, 179, 66)-net over F₄, using

t-expansion [i] based on digital (49, 179, 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]

(179−124, 179, 91)-Net over F₄ — Digital

Digital (55, 179, 91)-net over F₄, using

t-expansion [i] based on digital (50, 179, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(179−124, 179, 387)-Net in Base 4 — Upper bound on s

There is no (55, 179, 388)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 622346 766349 463085 190484 357695 863300 733544 135772 516938 892640 427772 004802 856552 389099 938112 428609 549507 138144 > 4¹⁷⁹ [i]