MinT - Best Known (68, 99, s)-Nets in Base 7

Best Known (68, 99, s)-Nets in Base 7

(68, 99, 206)-Net over F₇ — Constructive and digital

Digital (68, 99, 206)-net over F₇, using

7¹ times duplication [i] based on digital (67, 98, 206)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 32, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 16, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (35, 66, 104)-net over F₇, using
    - trace code for nets [i] based on digital (2, 33, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
        Niederreiter sequence [i]

(68, 99, 1249)-Net over F₇ — Digital

Digital (68, 99, 1249)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 99, 355558)-Net in Base 7 — Upper bound on s

There is no (68, 99, 355559)-net in base 7, because

1 times m-reduction [i] would yield (68, 98, 355559)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 66011 307878 829960 217971 485938 605122 145247 758515 324419 764520 585101 555353 344757 793895 > 7⁹⁸ [i]