MinT - Best Known (98, 98+32, s)-Nets in Base 4

Best Known (98, 98+32, s)-Nets in Base 4

(98, 98+32, 1028)-Net over F₄ — Constructive and digital

Digital (98, 130, 1028)-net over F₄, using

4² times duplication [i] based on digital (96, 128, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 32, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(98, 98+32, 1401)-Net over F₄ — Digital

Digital (98, 130, 1401)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+32, 176653)-Net in Base 4 — Upper bound on s

There is no (98, 130, 176654)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 852681 909971 848428 374872 633657 557119 804569 962446 755178 161584 205769 568874 278432 > 4¹³⁰ [i]