MinT - Best Known (45, 45+34, s)-Nets in Base 7

Best Known (45, 45+34, s)-Nets in Base 7

(45, 45+34, 110)-Net over F₇ — Constructive and digital

Digital (45, 79, 110)-net over F₇, using

1 times m-reduction [i] based on digital (45, 80, 110)-net over F₇, using
- trace code for nets [i] based on digital (5, 40, 55)-net over F₄₉, using
  - net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(45, 45+34, 229)-Net over F₇ — Digital

Digital (45, 79, 229)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+34, 10105)-Net in Base 7 — Upper bound on s

There is no (45, 79, 10106)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 5 797731 399771 698878 692910 932537 348854 617199 625184 728836 793291 990205 > 7⁷⁹ [i]