MinT - Best Known (175−114, 175, s)-Nets in Base 4

Best Known (175−114, 175, s)-Nets in Base 4

(175−114, 175, 66)-Net over F₄ — Constructive and digital

Digital (61, 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]

(175−114, 175, 99)-Net over F₄ — Digital

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]

(175−114, 175, 473)-Net in Base 4 — Upper bound on s

There is no (61, 175, 474)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2366 251014 420531 646452 452793 508028 141200 034575 604699 812795 031648 812093 742659 787995 328578 750086 203718 705850 > 4¹⁷⁵ [i]