MinT - Best Known (89−31, 89, s)-Nets in Base 7

Best Known (89−31, 89, s)-Nets in Base 7

(89−31, 89, 126)-Net over F₇ — Constructive and digital

Digital (58, 89, 126)-net over F₇, using

1 times m-reduction [i] based on digital (58, 90, 126)-net over F₇, using
- trace code for nets [i] based on digital (13, 45, 63)-net over F₄₉, using
  - net from sequence [i] based on digital (13, 62)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(89−31, 89, 660)-Net over F₇ — Digital

Digital (58, 89, 660)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−31, 89, 97158)-Net in Base 7 — Upper bound on s

There is no (58, 89, 97159)-net in base 7, because

1 times m-reduction [i] would yield (58, 88, 97159)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 233 696173 887605 479341 880332 023714 281877 899179 575628 768814 026747 242812 438375 > 7⁸⁸ [i]