MinT - Best Known (44, 44+31, s)-Nets in Base 7

Best Known (44, 44+31, s)-Nets in Base 7

(44, 44+31, 112)-Net over F₇ — Constructive and digital

Digital (44, 75, 112)-net over F₇, using

1 times m-reduction [i] based on digital (44, 76, 112)-net over F₇, using
- trace code for nets [i] based on digital (6, 38, 56)-net over F₄₉, using
  - net from sequence [i] based on digital (6, 55)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(44, 44+31, 264)-Net over F₇ — Digital

Digital (44, 75, 264)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+31, 15794)-Net in Base 7 — Upper bound on s

There is no (44, 75, 15795)-net in base 7, because

1 times m-reduction [i] would yield (44, 74, 15795)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 344 730556 999654 028275 505396 342087 143193 527400 604656 888353 581703 > 7⁷⁴ [i]