MinT - Best Known (72, 72+32, s)-Nets in Base 7

Best Known (72, 72+32, s)-Nets in Base 7

(72, 72+32, 208)-Net over F₇ — Constructive and digital

Digital (72, 104, 208)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (20, 36, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 18, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (36, 68, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 34, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(72, 72+32, 1431)-Net over F₇ — Digital

Digital (72, 104, 1431)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+32, 352786)-Net in Base 7 — Upper bound on s

There is no (72, 104, 352787)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7766 079437 959054 521420 877510 001791 280707 781236 230098 465138 784163 800863 666000 852015 483809 > 7¹⁰⁴ [i]