MinT - Best Known (88−28, 88, s)-Nets in Base 7

Best Known (88−28, 88, s)-Nets in Base 7

(88−28, 88, 204)-Net over F₇ — Constructive and digital

Digital (60, 88, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (16, 30, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 15, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (30, 58, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 29, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(88−28, 88, 1048)-Net over F₇ — Digital

Digital (60, 88, 1048)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−28, 88, 206696)-Net in Base 7 — Upper bound on s

There is no (60, 88, 206697)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 233 693917 393078 799008 201531 156965 652538 407583 193015 819190 883534 251496 235553 > 7⁸⁸ [i]