MinT - Best Known (75−32, 75, s)-Nets in Base 7

Best Known (75−32, 75, s)-Nets in Base 7

(75−32, 75, 110)-Net over F₇ — Constructive and digital

Digital (43, 75, 110)-net over F₇, using

1 times m-reduction [i] based on digital (43, 76, 110)-net over F₇, using
- trace code for nets [i] based on digital (5, 38, 55)-net over F₄₉, using
  - net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(75−32, 75, 229)-Net over F₇ — Digital

Digital (43, 75, 229)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−32, 75, 10359)-Net in Base 7 — Upper bound on s

There is no (43, 75, 10360)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2411 959438 562587 250610 244273 105686 370089 699147 260417 240807 606785 > 7⁷⁵ [i]