MinT - Best Known (104, 104+44, s)-Nets in Base 4

Best Known (104, 104+44, s)-Nets in Base 4

(104, 104+44, 384)-Net over F₄ — Constructive and digital

Digital (104, 148, 384)-net over F₄, using

4¹ times duplication [i] based on digital (103, 147, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 49, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(104, 104+44, 675)-Net over F₄ — Digital

Digital (104, 148, 675)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+44, 33862)-Net in Base 4 — Upper bound on s

There is no (104, 148, 33863)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127318 006823 152158 856254 453677 264381 511008 846395 048264 337114 766433 065430 322694 806886 014668 > 4¹⁴⁸ [i]