MinT - Best Known (81, 81+24, s)-Nets in Base 4

Best Known (81, 81+24, s)-Nets in Base 4

(81, 81+24, 1036)-Net over F₄ — Constructive and digital

Digital (81, 105, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (80, 104, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 26, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(81, 81+24, 1773)-Net over F₄ — Digital

Digital (81, 105, 1773)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+24, 326777)-Net in Base 4 — Upper bound on s

There is no (81, 105, 326778)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1645 520593 352311 509610 764856 154450 374598 589018 772038 961749 088228 > 4¹⁰⁵ [i]