MinT - Best Known (97−30, 97, s)-Nets in Base 16

Best Known (97−30, 97, s)-Nets in Base 16

(97−30, 97, 1034)-Net over F₁₆ — Constructive and digital

Digital (67, 97, 1034)-net over F₁₆, using

1 times m-reduction [i] based on digital (67, 98, 1034)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 32, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 16, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (35, 66, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 33, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(97−30, 97, 8305)-Net over F₁₆ — Digital

Digital (67, 97, 8305)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−30, 97, large)-Net in Base 16 — Upper bound on s

There is no (67, 97, large)-net in base 16, because

28 times m-reduction [i] would yield (67, 69, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]