MinT - Best Known (75−28, 75, s)-Nets in Base 7

Best Known (75−28, 75, s)-Nets in Base 7

(75−28, 75, 118)-Net over F₇ — Constructive and digital

Digital (47, 75, 118)-net over F₇, using

1 times m-reduction [i] based on digital (47, 76, 118)-net over F₇, using
- trace code for nets [i] based on digital (9, 38, 59)-net over F₄₉, using
  - net from sequence [i] based on digital (9, 58)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(75−28, 75, 419)-Net over F₇ — Digital

Digital (47, 75, 419)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−28, 75, 33923)-Net in Base 7 — Upper bound on s

There is no (47, 75, 33924)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2412 074697 748534 297699 425603 821815 295626 907313 811675 321492 145017 > 7⁷⁵ [i]