MinT - Best Known (38, 38+35, s)-Nets in Base 7

Best Known (38, 38+35, s)-Nets in Base 7

(38, 38+35, 102)-Net over F₇ — Constructive and digital

Digital (38, 73, 102)-net over F₇, using

1 times m-reduction [i] based on digital (38, 74, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 37, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(38, 38+35, 139)-Net over F₇ — Digital

Digital (38, 73, 139)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+35, 4528)-Net in Base 7 — Upper bound on s

There is no (38, 73, 4529)-net in base 7, because

1 times m-reduction [i] would yield (38, 72, 4529)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7 033434 407309 202000 228695 631368 301866 530842 805352 005026 782887 > 7⁷² [i]