MinT - Best Known (164, 164+50, s)-Nets in Base 4

Best Known (164, 164+50, s)-Nets in Base 4

(164, 164+50, 1040)-Net over F₄ — Constructive and digital

Digital (164, 214, 1040)-net over F₄, using

4² times duplication [i] based on digital (162, 212, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 53, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(164, 164+50, 2738)-Net over F₄ — Digital

Digital (164, 214, 2738)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+50, 483192)-Net in Base 4 — Upper bound on s

There is no (164, 214, 483193)-net in base 4, because

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]