MinT - Best Known (205−122, 205, s)-Nets in Base 4

Best Known (205−122, 205, s)-Nets in Base 4

(205−122, 205, 104)-Net over F₄ — Constructive and digital

Digital (83, 205, 104)-net over F₄, using

t-expansion [i] based on digital (73, 205, 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]

(205−122, 205, 129)-Net over F₄ — Digital

Digital (83, 205, 129)-net over F₄, using

t-expansion [i] based on digital (81, 205, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(205−122, 205, 779)-Net in Base 4 — Upper bound on s

There is no (83, 205, 780)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2736 394309 345786 424575 676634 073999 159403 879236 163059 932426 136591 651207 092628 765226 579982 132422 411198 529856 663033 485425 786560 > 4²⁰⁵ [i]