MinT - Best Known (58, 58+39, s)-Nets in Base 16

Best Known (58, 58+39, s)-Nets in Base 16

(58, 58+39, 532)-Net over F₁₆ — Constructive and digital

Digital (58, 97, 532)-net over F₁₆, using

1 times m-reduction [i] based on digital (58, 98, 532)-net over F₁₆, using
- trace code for nets [i] based on digital (9, 49, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(58, 58+39, 1206)-Net over F₁₆ — Digital

Digital (58, 97, 1206)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+39, 641345)-Net in Base 16 — Upper bound on s

There is no (58, 97, 641346)-net in base 16, because

1 times m-reduction [i] would yield (58, 96, 641346)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 402775 033767 390945 871385 423002 410408 508586 540392 918839 785451 913715 272097 320356 336556 827096 345306 670530 363491 242336 > 16⁹⁶ [i]