MinT - Best Known (222−101, 222, s)-Nets in Base 4

Best Known (222−101, 222, s)-Nets in Base 4

(222−101, 222, 130)-Net over F₄ — Constructive and digital

Digital (121, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 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]

(222−101, 222, 212)-Net over F₄ — Digital

Digital (121, 222, 212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−101, 222, 2935)-Net in Base 4 — Upper bound on s

There is no (121, 222, 2936)-net in base 4, because

1 times m-reduction [i] would yield (121, 221, 2936)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 523063 268871 421400 335751 414978 717396 663927 132123 571362 757168 624521 203068 807754 130056 964074 060128 523765 429861 317052 554325 793647 857323 > 4²²¹ [i]