MinT - Best Known (72, 72+34, s)-Nets in Base 7

Best Known (72, 72+34, s)-Nets in Base 7

(72, 72+34, 204)-Net over F₇ — Constructive and digital

Digital (72, 106, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (19, 36, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 18, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (36, 70, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 35, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(72, 72+34, 1153)-Net over F₇ — Digital

Digital (72, 106, 1153)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+34, 222437)-Net in Base 7 — Upper bound on s

There is no (72, 106, 222438)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 380552 856218 226130 736196 218533 199731 436003 894259 794406 635488 042907 474674 745009 793778 963909 > 7¹⁰⁶ [i]