MinT - Best Known (64, 64+43, s)-Nets in Base 7

Best Known (64, 64+43, s)-Nets in Base 7

(64, 64+43, 120)-Net over F₇ — Constructive and digital

Digital (64, 107, 120)-net over F₇, using

1 times m-reduction [i] based on digital (64, 108, 120)-net over F₇, using
- trace code for nets [i] based on digital (10, 54, 60)-net over F₄₉, using
  - net from sequence [i] based on digital (10, 59)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(64, 64+43, 390)-Net over F₇ — Digital

Digital (64, 107, 390)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+43, 26659)-Net in Base 7 — Upper bound on s

There is no (64, 107, 26660)-net in base 7, because

1 times m-reduction [i] would yield (64, 106, 26660)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 380637 623929 779931 265210 144367 392723 823557 070904 039621 701146 909587 126361 823217 958786 047993 > 7¹⁰⁶ [i]