MinT - Best Known (74, 74+35, s)-Nets in Base 4

Best Known (74, 74+35, s)-Nets in Base 4

(74, 74+35, 240)-Net over F₄ — Constructive and digital

Digital (74, 109, 240)-net over F₄, using

4¹ times duplication [i] based on digital (73, 108, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 36, 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]

(74, 74+35, 388)-Net over F₄ — Digital

Digital (74, 109, 388)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+35, 15969)-Net in Base 4 — Upper bound on s

There is no (74, 109, 15970)-net in base 4, because

1 times m-reduction [i] would yield (74, 108, 15970)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 105314 885329 756453 798754 061121 853313 969193 199690 290266 644059 606222 > 4¹⁰⁸ [i]