MinT - Best Known (202−76, 202, s)-Nets in Base 4

Best Known (202−76, 202, s)-Nets in Base 4

(202−76, 202, 137)-Net over F₄ — Constructive and digital

Digital (126, 202, 137)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 53, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (73, 149, 104)-net over F₄, using
  - net from sequence [i] based on digital (73, 103)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
      - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(202−76, 202, 363)-Net over F₄ — Digital

Digital (126, 202, 363)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−76, 202, 7914)-Net in Base 4 — Upper bound on s

There is no (126, 202, 7915)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 493635 961325 948582 247598 457514 798507 155959 300892 265537 821233 269419 954058 208332 354506 381796 948969 696324 207558 307048 720286 > 4²⁰² [i]