MinT - Best Known (113, 113+37, s)-Nets in Base 4

Best Known (113, 113+37, s)-Nets in Base 4

(113, 113+37, 1028)-Net over F₄ — Constructive and digital

Digital (113, 150, 1028)-net over F₄, using

4² times duplication [i] based on digital (111, 148, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 37, 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]

(113, 113+37, 1553)-Net over F₄ — Digital

Digital (113, 150, 1553)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+37, 242494)-Net in Base 4 — Upper bound on s

There is no (113, 150, 242495)-net in base 4, because

1 times m-reduction [i] would yield (113, 149, 242495)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 509282 983548 047400 408339 265772 743764 455632 289307 507769 562184 986440 421324 395067 275381 645207 > 4¹⁴⁹ [i]