MinT - Best Known (75−36, 75, s)-Nets in Base 7

Best Known (75−36, 75, s)-Nets in Base 7

(75−36, 75, 102)-Net over F₇ — Constructive and digital

Digital (39, 75, 102)-net over F₇, using

1 times m-reduction [i] based on digital (39, 76, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 38, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(75−36, 75, 141)-Net over F₇ — Digital

Digital (39, 75, 141)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−36, 75, 4168)-Net in Base 7 — Upper bound on s

There is no (39, 75, 4169)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2412 516441 866995 436077 878644 482771 315853 850800 737543 175154 667969 > 7⁷⁵ [i]