MinT - Best Known (77−33, 77, s)-Nets in Base 7

Best Known (77−33, 77, s)-Nets in Base 7

(77−33, 77, 110)-Net over F₇ — Constructive and digital

Digital (44, 77, 110)-net over F₇, using

1 times m-reduction [i] based on digital (44, 78, 110)-net over F₇, using
- trace code for nets [i] based on digital (5, 39, 55)-net over F₄₉, using
  - net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(77−33, 77, 229)-Net over F₇ — Digital

Digital (44, 77, 229)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−33, 77, 11701)-Net in Base 7 — Upper bound on s

There is no (44, 77, 11702)-net in base 7, because

1 times m-reduction [i] would yield (44, 76, 11702)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 16904 198918 852806 715124 936163 619958 825552 663679 573949 654152 642849 > 7⁷⁶ [i]