MinT - Best Known (57, 57+100, s)-Nets in Base 4

Best Known (57, 57+100, s)-Nets in Base 4

(57, 57+100, 66)-Net over F₄ — Constructive and digital

Digital (57, 157, 66)-net over F₄, using

t-expansion [i] based on digital (49, 157, 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]

(57, 57+100, 91)-Net over F₄ — Digital

Digital (57, 157, 91)-net over F₄, using

t-expansion [i] based on digital (50, 157, 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]

(57, 57+100, 464)-Net in Base 4 — Upper bound on s

There is no (57, 157, 465)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34258 194898 033278 450371 573248 398128 669912 339035 185496 677925 113457 496768 797616 307981 839522 719360 > 4¹⁵⁷ [i]