MinT - Best Known (175−67, 175, s)-Nets in Base 4

Best Known (175−67, 175, s)-Nets in Base 4

(175−67, 175, 130)-Net over F₄ — Constructive and digital

Digital (108, 175, 130)-net over F₄, using

t-expansion [i] based on digital (105, 175, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(175−67, 175, 302)-Net over F₄ — Digital

Digital (108, 175, 302)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−67, 175, 6530)-Net in Base 4 — Upper bound on s

There is no (108, 175, 6531)-net in base 4, because

1 times m-reduction [i] would yield (108, 174, 6531)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 575 015064 422474 439614 755873 045496 203502 644941 687842 003953 072628 373195 694860 755594 486251 734246 342938 773576 > 4¹⁷⁴ [i]