MinT - Best Known (164, 164+51, s)-Nets in Base 4

Best Known (164, 164+51, s)-Nets in Base 4

(164, 164+51, 1036)-Net over F₄ — Constructive and digital

Digital (164, 215, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (164, 216, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 54, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(164, 164+51, 2545)-Net over F₄ — Digital

Digital (164, 215, 2545)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+51, 483192)-Net in Base 4 — Upper bound on s

There is no (164, 215, 483193)-net in base 4, because

1 times m-reduction [i] would yield (164, 214, 483193)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 199776 510555 352583 238391 053371 020068 580258 720383 190710 632275 158972 757485 117727 862412 518813 498261 338097 151990 387201 494508 942460 > 4²¹⁴ [i]