MinT - Best Known (56, 56+37, s)-Nets in Base 7

Best Known (56, 56+37, s)-Nets in Base 7

(56, 56+37, 118)-Net over F₇ — Constructive and digital

Digital (56, 93, 118)-net over F₇, using

1 times m-reduction [i] based on digital (56, 94, 118)-net over F₇, using
- trace code for nets [i] based on digital (9, 47, 59)-net over F₄₉, using
  - net from sequence [i] based on digital (9, 58)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(56, 56+37, 367)-Net over F₇ — Digital

Digital (56, 93, 367)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+37, 26252)-Net in Base 7 — Upper bound on s

There is no (56, 93, 26253)-net in base 7, because

1 times m-reduction [i] would yield (56, 92, 26253)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 561080 883590 931708 085849 452267 953617 552898 492891 091750 803082 321387 619833 268969 > 7⁹² [i]