MinT - Best Known (148, 148+37, s)-Nets in Base 4

Best Known (148, 148+37, s)-Nets in Base 4

(148, 148+37, 1065)-Net over F₄ — Constructive and digital

Digital (148, 185, 1065)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 33, 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 (115, 152, 1032)-net over F₄, using
  - trace code for nets [i] based on digital (1, 38, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(148, 148+37, 5927)-Net over F₄ — Digital

Digital (148, 185, 5927)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+37, 3592510)-Net in Base 4 — Upper bound on s

There is no (148, 185, 3592511)-net in base 4, because

1 times m-reduction [i] would yield (148, 184, 3592511)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601 227774 401407 175014 760355 894407 998272 064293 665053 738159 840321 279944 209587 259869 269396 393391 810063 996372 460215 > 4¹⁸⁴ [i]