MinT - Best Known (203−41, 203, s)-Nets in Base 4

Best Known (203−41, 203, s)-Nets in Base 4

(203−41, 203, 1065)-Net over F₄ — Constructive and digital

Digital (162, 203, 1065)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 35, 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 (127, 168, 1032)-net over F₄, using
  - trace code for nets [i] based on digital (1, 42, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(203−41, 203, 5992)-Net over F₄ — Digital

Digital (162, 203, 5992)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−41, 203, 3334178)-Net in Base 4 — Upper bound on s

There is no (162, 203, 3334179)-net in base 4, because

1 times m-reduction [i] would yield (162, 202, 3334179)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 316243 617842 713118 123210 597703 869748 760247 868136 638886 855929 805551 372333 191233 364103 293151 048502 203024 782070 172403 637656 > 4²⁰² [i]