MinT - Best Known (44, 44+36, s)-Nets in Base 7

Best Known (44, 44+36, s)-Nets in Base 7

(44, 44+36, 108)-Net over F₇ — Constructive and digital

Digital (44, 80, 108)-net over F₇, using

trace code for nets [i] based on digital (4, 40, 54)-net over F₄₉, using
- net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(44, 44+36, 192)-Net over F₇ — Digital

Digital (44, 80, 192)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+36, 7165)-Net in Base 7 — Upper bound on s

There is no (44, 80, 7166)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 40 540822 504844 123071 152952 497585 472520 776061 724606 432938 740461 894829 > 7⁸⁰ [i]