MinT - Best Known (242−109, 242, s)-Nets in Base 4

Best Known (242−109, 242, s)-Nets in Base 4

(242−109, 242, 130)-Net over F₄ — Constructive and digital

Digital (133, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(242−109, 242, 236)-Net over F₄ — Digital

Digital (133, 242, 236)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−109, 242, 3355)-Net in Base 4 — Upper bound on s

There is no (133, 242, 3356)-net in base 4, because

1 times m-reduction [i] would yield (133, 241, 3356)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 676935 202160 677473 193288 629558 433547 549679 796613 249578 445172 131072 072201 457225 300692 386696 644211 233580 312244 020963 875430 039410 105864 273076 095376 > 4²⁴¹ [i]