MinT - Best Known (46, 46+19, s)-Nets in Base 4

Best Known (46, 46+19, s)-Nets in Base 4

(46, 46+19, 240)-Net over F₄ — Constructive and digital

Digital (46, 65, 240)-net over F₄, using

t-expansion [i] based on digital (45, 65, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (45, 66, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 22, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(46, 46+19, 385)-Net over F₄ — Digital

Digital (46, 65, 385)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+19, 26413)-Net in Base 4 — Upper bound on s

There is no (46, 65, 26414)-net in base 4, because

1 times m-reduction [i] would yield (46, 64, 26414)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 340 307414 085429 260115 278650 598549 639305 > 4⁶⁴ [i]