MinT - Best Known (93−28, 93, s)-Nets in Base 7

Best Known (93−28, 93, s)-Nets in Base 7

(93−28, 93, 208)-Net over F₇ — Constructive and digital

Digital (65, 93, 208)-net over F₇, using

1 times m-reduction [i] based on digital (65, 94, 208)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (18, 32, 104)-net over F₇, using
    - trace code for nets [i] based on digital (2, 16, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (33, 62, 104)-net over F₇, using
    - trace code for nets [i] based on digital (2, 31, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(93−28, 93, 1496)-Net over F₇ — Digital

Digital (65, 93, 1496)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−28, 93, 414154)-Net in Base 7 — Upper bound on s

There is no (65, 93, 414155)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 927530 401620 502231 307891 310165 143618 406686 248942 840449 337175 601342 091707 529669 > 7⁹³ [i]