MinT - Best Known (107−37, 107, s)-Nets in Base 7

Best Known (107−37, 107, s)-Nets in Base 7

(107−37, 107, 132)-Net over F₇ — Constructive and digital

Digital (70, 107, 132)-net over F₇, using

1 times m-reduction [i] based on digital (70, 108, 132)-net over F₇, using
- trace code for nets [i] based on digital (16, 54, 66)-net over F₄₉, using
  - net from sequence [i] based on digital (16, 65)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(107−37, 107, 791)-Net over F₇ — Digital

Digital (70, 107, 791)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−37, 107, 119295)-Net in Base 7 — Upper bound on s

There is no (70, 107, 119296)-net in base 7, because

1 times m-reduction [i] would yield (70, 106, 119296)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 380540 497490 235086 277256 002778 640641 190626 955114 365204 972787 141790 863335 217292 159779 331073 > 7¹⁰⁶ [i]