MinT - Best Known (70−24, 70, s)-Nets in Base 7

Best Known (70−24, 70, s)-Nets in Base 7

(70−24, 70, 128)-Net over F₇ — Constructive and digital

Digital (46, 70, 128)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (8, 20, 26)-net over F₇, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 7, 13)-net over F₇, using
      - 6 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
    2. digital (1, 13, 13)-net over F₇ (see above)
2. digital (26, 50, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 25, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(70−24, 70, 598)-Net over F₇ — Digital

Digital (46, 70, 598)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−24, 70, 74973)-Net in Base 7 — Upper bound on s

There is no (46, 70, 74974)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 143524 986128 033590 769730 974827 572902 440688 729037 819395 193529 > 7⁷⁰ [i]